What is Beta Distribution?

A continuous probability distribution defined on the interval [0, 1] parametrized by two positive shape parameters, α and β.

Often used in Bayesian inference to model beliefs about probability (e.g., success rate of a new drug) and in project management (PERT).

What do α and β control?

α > 1 & β > 1 gives a bell shape. α < 1 & β < 1 gives a U-shape. α = β = 1 is Uniform [0,1].

Beta Distribution Calculator

Calculate probability density and properties for range [0, 1].

Shape Alpha (α)

Shape Beta (β)

Target Value (x)

0 <= x <= 1

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CDF F(0.5)

0

PDF f(0.5) = 0

Distribution Curve (PDF)

Mean

Variance

Formulas

PDF

Mean

Variance

Frequently Asked Questions

About the Beta Distribution

What it calculates

This beta distribution solves mathematical and statistical problems using standard formulas. Probability on interval [0, 1].

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Beta Distribution.

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Beta Distribution Calculator

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Distribution Curve (PDF)

About the Beta Distribution

Related Calculators

Cauchy

Exponential

Gamma Distribution

Log-Normal

Normal Distribution

Pareto